I mostly trail ride by myself; so a horse that will hack out by itself is pretty much a requirement for me.
It is not, IMO, something you can train into a horse, or for that matter, a rider, if the necessary qualities are not already there.
The horse has to be a leader, or an alpha horse, not dependent, not barn bound or buddy sour. The correct type of horse is forward and easy to keep in front of your leg.
If you have a horse with these qualities, and you put a tentative or tense rider on it, who doesn't take the alpha role, who holds their breath or startles easily, they will eventually persuade the horse that those noises in the bushes are cougars ready to pounce.
Of my two current horses, the big chestnut gelding tends to be a little more mischievous and playful when out by himself, his natural smart aleck comes out, but he doesn't spook or shy and he's forward and relaxed.
The little bay gelding, the husband/guest/child horse, will go out alone but he doesn't like it. He won't put a foot wrong but he'll yell for his barn buddies and turn back any chance he gets. I would not ride him out by himself on a regular basis, on an occasional basis he does fine.
If your horse spooks, shies, props or is "looky" in the ring or when being ridden in a group, or if you're not a very secure, assertive rider, don't even try taking her out by herself.